feat: close remaining gaps — middleware, demo wiring, error UX, env validation

- Auth: middleware.ts guards /protected via better-auth session cookie;
  protected page reads session server-side (auth.api.getSession)
- Demo wiring (app/demo + components/demo): react-markdown + remark-gfm +
  shiki CodeBlock, RHF+zod form with react-query mutation + sonner toast,
  react-table items list (legacy API, table v9), /api/items GET+POST
  (zod v4 coercion, schema in lib/items.ts shared with unit tests)
- Error UX: app/error.tsx (retry + digest), not-found.tsx (404), loading.tsx
- Env: lib/env.ts zod-validated (no import-time throw), .env.example sync
  (NEXT_PUBLIC_BETTER_AUTH_URL), auth-client uses env
- Tooling: @vitest/coverage-v8 (test:coverage works), tsconfig cleanup
  (drop .next/dev/dev/types artifact), README rewrite, demo e2e specs

lib/auth-client.ts

@@ -1,7 +1,8 @@
 import { createAuthClient } from "better-auth/react";
+import { env } from "@/lib/env";
 
 export const authClient = createAuthClient({
-  baseURL: process.env.NEXT_PUBLIC_BETTER_AUTH_URL ?? "http://localhost:3000",
+  baseURL: env.NEXT_PUBLIC_BETTER_AUTH_URL,
 });
 
 export const { useSession, signIn, signUp, signOut } = authClient;